Unformatted text preview: FINA0301 Derivatives Dr. Huiyan Qiu Homework Assignment #1 Due: January 31, Monday, drop in Clive’s box by 6PM 1. Suppose you desire to short‐sell 400 shares of JKI stock, which has a bid price of $25.12 and an ask price of $25.31. You cover the short position 180 days later when the bid price is $22.87 and the ask price is $23.06. (a) Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you earn? (b) Suppose that there is a 0.3% commission to engage in the short‐sale (this is the commission to sell the stock) and a 0.3% commission to close the short‐sale (this is the commission to buy the stock back). How do these commissions change the profit in the previous answer? (c) Suppose the 6‐month interest rate is 3% and that you are paid nothing on the short‐
sale proceeds. How much interest do you lose during the 6 months in which you have the short position? 2. (a) Suppose you enter into a long 6‐month forward position at a forward price of $50. What is the payoff in 6 months for prices of $40, $45, $50, $55, and $60? (b) Suppose you buy a 6‐month call option with a strike price of $50. What is the payoff in 6 months at the same prices for the underlying asset? (c) Comparing the payoffs of parts (a) and (b), which contract should be more expensive (i.e. the long call or long forward)? Why? 3. Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1‐year effective annual interest rate is 10%. (a) Graph the payoff and profit diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why? 4. Suppose the stock price is $40 and the effective annual interest rate is 8%. Draw payoff and profit diagrams for the following options: (a) 35‐strike put with a premium of $1.53. (b) 40‐strike put with a premium of $3.26. (c) 45‐strike put with a premium of $5.75. Consider your payoff diagram with all three options graphed together. Intuitively, why should the option premium increase with the strike price? 1 FINA0301 Derivatives Dr. Huiyan Qiu For the following problems (Q5‐6) assume the effective 6‐month interest rate is 2% and the S&R 6‐month forward price is $1020, and use these premiums for S&R options with 6 months to expiration: Strike
$950 $120.405 $51.777 1000 93.809 74.201 1020 84.470 84.470 1050 71.802 101.214 1107 51.873 137.167 5. Construct payoff and profit diagrams for the purchase of a 950‐strike S&R call and sale of a 1000‐strike S&R call. Verify that you obtain exactly the same profit diagram for the purchase of a 950‐strike S&R put and sale of a 1000‐strike S&R put. What is the difference in the payoff diagrams for the call and put spreads? Why is there a difference? 6. Compute profit diagrams for the following ratio spreads: (a) Buy 950‐strike call, sell two 1050‐strike calls. (b) Buy two 950‐strike calls, sell three 1050‐strike calls. (c) Consider buying n 950‐strike calls and selling m 1050‐strike calls so that the premium of the position is zero. Considering your analysis in (a) and (b), what can you say about n/m? What exact ratio gives you a zero premium? 7. Find a future contract or a call option or a put option existing in Hong Kong market. Answer the following questions. (a) Where do you find the information of the derivative security? (Best place to look: the website of Hong Kong Exchanges and Clearing Limited or newspaper.) (b) Provide some description of the derivative security. (Make your own choice on how much information to provide.) (c) Offer market information of the derivative product on one of the trading days between January 17 and February 1. The information should include but not limited to the price and volume. 2 ...
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